Get Answers to all your Questions

Filter By

Clear Filter

All Questions

#6.2

The ratio of the corresponding altitudes of two similar triangles is 3/5. Is it correct to say that ratio of their areas is 6/5? Why?

Answer: [False]

Given:- Ratio of corresponding altitudes of two similar triangles is 3/5

As we know that the ratio of the areas of two similar triangles is equal to the ratio of squares of any two corresponding altitudes.

$\therefore \frac{\text {Area 1}}{\text {Area 2}}=\left ( \frac{\text {Altitude 1}}{\text {Altitude 2}} \right )^{2}$

$\frac{\text {Area 1}}{\text {Area 2}}=\left ( \frac{3}{5} \right )^{2}$ $\left [ Q\frac{\text {Altitude 1}}{\text {Altitude 2}}=\frac{3}{5} \right ]$

$=\frac{9}{25}$

Hence the given statement is false because ratio of areas of two triangles is 9/25 which is not equal to 6/5

View Full Answer(1)

Posted by

infoexpert23

#6.2

If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, can you say that the two triangles will be similar? Why?

Answer : [True]

Let two right angle triangles are ABC and PQR.

Given:- One of the acute angle of one triangle is equal to an acute angle of the other triangle.

$\text {In}\Delta ABC \; \text {and}\; \Delta PQR$

$\\\angle B = \angle Q = 90^{o}\\\angle C = \angle R = x^{o}$

In $\Delta ABC$

$\angle A + \angle B + \angle C = 180^{o}$

[Sum of interior angles of a triangle is 180°]

$\angle A + 90^{o}+ x^{o} = 180^{o}$

$\angle A + 90^{o}- x^{o} \; \; \; \; \; \; \; \; \; ....(1)$

Also in $\Delta PQR$

$\angle P + \angle Q + \angle R = 180^{o}$

$\angle P + 90^{o}- x^{o} = 180^{o}$

$\angle P = 90^{o}- x^{o} \; \; \; \; \; \; .....(2)$

from equation (1) and (2)

$\angle A=\angle P \; \; \; \; \; \; .....(3)$

from equation (1), (2) and (3) are observed that corresponding angles of the triangles are equal therefore triangle are similar.

View Full Answer(1)

Posted by

infoexpert23

Crack CUET with india's "Best Teachers"

HD Video Lectures
Unlimited Mock Tests
Faculty Support

#6.2

D is a point on side QR of $\Delta$ PQR such that PD $\perp$ QR. Will it be correct to say that $\Delta$ PQD ~ $\Delta$ RPD? Why?

Answer : [False]

In $\Delta$ PQD and $\Delta$ RPD

$PD = PD$ (common side)

$\angle PDQ = \angle PDR$ (each 90^o)

The given statement $\Delta PQD \sim \Delta RPD$ is false.

Because according to the definition of similarity two triangles are similar, if their corresponding angles are equal and their corresponding sides are in the same ratio

View Full Answer(1)

Posted by

infoexpert23

#6.2

In Fig., if $\angle$ D = $\angle$ C, then is it true that $\Delta ADE \sim \Delta ACB$ ? Why?

Answer : [True]

In $\Delta$ ADE and $\Delta$ ACB

$\angle D=\angle C$ (given)

$\angle A = \angle A$ (common angle)

And we know that if two angles of one triangle are equal to the two angles of another triangle, then the two triangles are similar by AA similarity criteria.

$\therefore$ $\Delta ADE \sim \Delta ACB$ {by AA similarity criterion}

Hence the given statement is true.

View Full Answer(1)

Posted by

infoexpert23

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

#6.2

Is it true to say that if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar? Give reasons for your answer.

Answer. [False]

Given:- (1) An angle of one triangle is equal to an angle of another triangle.

(2) Two sides of one triangle are proportional to the two sides of the other triangle.

According to SAS similarity criterion if one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in the same ratio, then the triangles are similar.

But here, the given statement is false because one angle and two sides of two triangles are equal but these sides not including equal angle.

View Full Answer(1)

Posted by

infoexpert23

#6.2

Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?

Answer: True

According to question,

$AB = 3PQ \; \; \; \; \; \; ...(1)$

$AC = 3PR \; \; \; \; \;...(2)$

also the perimeter of $\Delta$ ABC is three times the perimeter of $\Delta$ PQR

$AB + BC + CA = 3(PQ + QR + RP)$

$AB + BC + CA = 3PQ + 3QR + 3RP$

$3PQ + BC + 3PR = 3PQ + 3QR + 3PR$ (using eq. (1) and (2))

$BC=3QR\; \; \; \; \; \; .....(3)$

from equation (1), (2) and (3) we conclude that sides of both the triangles are in the same ratio.

As we know that if the corresponding sides of two triangles are in the same ratio, then the triangles are similar by SSS similarity criterion

Hence given statement is true.

View Full Answer(1)

Posted by

infoexpert23

NEET 2024 Most scoring concepts

Just Study 32% of the NEET syllabus and Score up to 100% marks

#6.2

Is the following statement true? Why? “Two quadrilaterals are similar, if their corresponding angles are equal”.

Answer: [False]

Quadrilateral:- A quadrilateral can be defined as a closed, two-dimensional shape which has four straight sides. We can find the shape of quadrilaterals in various things around us, like in a chessboard, a kite etc. The given statement "Two quadrilaterals are similar if their corresponding angles are equal" is not true because. Two quadrilaterals are similar if and only if their corresponding angles are equal and the ratio of their corresponding sides are also equal.

View Full Answer(1)

Posted by

infoexpert23

#6.2

In triangles PQR and MST, $\angle$ P = 55°, $\angle$ Q = 25°, $\angle$ M = 100° and $\angle$ S = 25°. Is $\Delta$ QPR $\sim$ $\Delta$ TSM? Why?

Answer: [False]

$\Delta PQR, \angle P + \angle Q + \angle R = 180^{o}$ $\text{ ({Interior angle of triangle}) }$

$55+25+\angle R=180$

$\angle R=180-80$

$\angle R=100^{o}$

$\text{In }$ $\Delta TSM, \angle T + \angle S + \angle M = 180^{o}$ $\text{[Interior angle of the triangle] }$

$\angle T + 25^{o}+100^{o}=180^{o}$

$\angle T =180^{o}-125$

$\angle T =55^{o}$

$\text{In }$ $\Delta PQR$ $\text{and }$ $\Delta TSM$

$\angle P=\angle T$

$\angle Q=\angle S$

$\angle R=\angle M$

Also are know that if all corresponding angles of two triangles are equal then triangles are similar.

$\therefore \Delta PQR\sim \Delta TSM$

Hence given statement is false because $\angle$ QPR is not similar to $\angle$ TSM.

View Full Answer(1)

Posted by

infoexpert23

Crack CUET with india's "Best Teachers"

HD Video Lectures
Unlimited Mock Tests
Faculty Support

#6.2

In Fig 6.4, BD and CE intersect each other at the point P. Is $\Delta$ PBC $\sim$ $\Delta$ PDE? Why?

Answer : [True]

Given:- BD and CE intersect each other at point P.

$\text{Here, }$ $\angle BPC=\angle EPD$ $\text{[Vertically opposite angle] }$

$\frac{BP}{PD}=\frac{5}{10}=\frac{1}{2}$

$\frac{PC}{PE}=\frac{6}{12}=\frac{1}{2}$

$\frac{BP}{PD}=\frac{PC}{PE}$

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in the same ratio.

$\text{Also in }$ $\Delta PBC$ $\text{ and }$ $\Delta PDE$

$\frac{BP}{PD}=\frac{PC}{PE}\; and\; \angle BPC=\angle EPD$

$\therefore \Delta PBC\sim \Delta PDE$

Hence given statement is true.

View Full Answer(1)

Posted by

infoexpert23

#6.2

A and B are respectively the points on the sides PQ and PR of a triangle PQR such that PQ = 12.5 cm, PA = 5 cm, BR= 6 cm and PB = 4 cm. Is AB || QR?

Give reasons for your answer.

Answer : [True]

Given: PQ = 12.5 cm, PA = 5 cm, BR = 6 cm and PB = 4 cm

QA = QP – PA = 12.5 – 5 = 7.5 cm

$\frac{PA}{AQ}=\frac{5}{7.5}=\frac{50}{75}=\frac{2}{3}$

$\frac{PB}{PR}=\frac{4}{6}=\frac{2}{3}$

Here

$\frac{PA}{AQ}=\frac{PB}{PR}$

According to Converse of basic proportionality theorem if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

$\therefore AB\parallel QR$

View Full Answer(1)

Posted by

infoexpert23

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Exams

Colleges

Predictors

Resources

Quick links

Quick Links

Exams

Colleges

Resources

Colleges

Resources

Exams

Exams

Colleges

Resources

Diploma Colleges

Other Exams

Exams

Resources

Upcoming Events

Exams

Ranking

Products & Resources

NCERT Solutions

Top Countries

Student Visas

Exams

Colleges

Exams

Colleges

Upcoming Events

Resources

Exams

Colleges & Courses

Predictors

Resources

Online Courses

Products

Engineering Preparation

Medical Preparation

Top Streams

Specializations

Resources

Top Providers

Exams

Colleges

Predictors

Resources

Resources

Exams

Colleges

Predictors & E-Books

Exams

Animation Courses

Colleges

Resources

Exams

Colleges

Resources

Top Courses & Careers

Colleges

Exams

Resources

Get Answers to all your Questions

All Questions

The ratio of the corresponding altitudes of two similar triangles is 3/5. Is it correct to say that ratio of their areas is 6/5? Why?

Posted by

infoexpert23

If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, can you say that the two triangles will be similar? Why?

Posted by

infoexpert23

Crack CUET with india's "Best Teachers"

D is a point on side QR of PQR such that PD QR. Will it be correct to say that PQD ~ RPD? Why?

Posted by

infoexpert23

In Fig., if D = C, then is it true that ? Why?

Posted by

infoexpert23

JEE Main high-scoring chapters and topics

Is it true to say that if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar? Give reasons for your answer.

D is a point on side QR of $\Delta$ PQR such that PD $\perp$ QR. Will it be correct to say that $\Delta$ PQD ~ $\Delta$ RPD? Why?

In Fig., if $\angle$ D = $\angle$ C, then is it true that $\Delta ADE \sim \Delta ACB$ ? Why?

In triangles PQR and MST, $\angle$ P = 55°, $\angle$ Q = 25°, $\angle$ M = 100° and $\angle$ S = 25°. Is $\Delta$ QPR $\sim$ $\Delta$ TSM? Why?

In Fig 6.4, BD and CE intersect each other at the point P. Is $\Delta$ PBC $\sim$ $\Delta$ PDE? Why?

A and B are respectively the points on the sides PQ and PR of a triangle PQR such that PQ = 12.5 cm, PA = 5 cm, BR= 6 cm and PB = 4 cm. Is AB || QR?

Give reasons for your answer.